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Questions and Answers
The formula for the sum of forces in the x-direction is ∑𝐹𝑥 = m𝑎______.
The formula for the sum of forces in the x-direction is ∑𝐹𝑥 = m𝑎______.
x
The unit of force is the ______.
The unit of force is the ______.
Newton
Impulse is equal to the product of force and the change in ______.
Impulse is equal to the product of force and the change in ______.
time
According to Newton's Third Law, every action has an equal and opposite ______.
According to Newton's Third Law, every action has an equal and opposite ______.
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The principle stating that the total force experienced by a body is the vector sum of all the forces acting on it is called the ______ principle.
The principle stating that the total force experienced by a body is the vector sum of all the forces acting on it is called the ______ principle.
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Momentum is calculated using the formula ______ = m𝑣.
Momentum is calculated using the formula ______ = m𝑣.
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The SI unit of momentum is kg______s-1.
The SI unit of momentum is kg______s-1.
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The two forces in an action-reaction pair act on ______ objects.
The two forces in an action-reaction pair act on ______ objects.
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The formula for maximum height (H) can be expressed as H = 𝑢( _______ )sinθ.
The formula for maximum height (H) can be expressed as H = 𝑢( _______ )sinθ.
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The time of flight (T) is given by T = _______ / g.
The time of flight (T) is given by T = _______ / g.
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Time is the change in ______.
Time is the change in ______.
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The range (R) of the projectile can be expressed as R = _______ / g.
The range (R) of the projectile can be expressed as R = _______ / g.
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At the time of flight, the j-component of the displacement is _______.
At the time of flight, the j-component of the displacement is _______.
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The area under the graph of velocity vs. time is the ______.
The area under the graph of velocity vs. time is the ______.
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The maximum range occurs when sin²θ = _______.
The maximum range occurs when sin²θ = _______.
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The term ______ and velocity are often used interchangeably.
The term ______ and velocity are often used interchangeably.
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The angle for maximum range of the projectile is _______ degrees.
The angle for maximum range of the projectile is _______ degrees.
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Average speed and average velocity have the same magnitude when the motion is in ______ direction.
Average speed and average velocity have the same magnitude when the motion is in ______ direction.
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The formula for the vertical component of displacement during flight is 1/2 g t² = u sinθ t - _______.
The formula for the vertical component of displacement during flight is 1/2 g t² = u sinθ t - _______.
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A runner accelerates uniformly with an acceleration of 2 m/s² from ______ for a time of 3 s.
A runner accelerates uniformly with an acceleration of 2 m/s² from ______ for a time of 3 s.
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During a 5 s time interval, a person's position changes from 𝑥₁ = 100 m to 𝑥₂ = ______.
During a 5 s time interval, a person's position changes from 𝑥₁ = 100 m to 𝑥₂ = ______.
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The expression for the range can be simplified to R = _______ u² sin²θ.
The expression for the range can be simplified to R = _______ u² sin²θ.
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Kinematic equations are used in tools for analyzing ______ motion.
Kinematic equations are used in tools for analyzing ______ motion.
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The ______ is a positive number with units denoting how fast an object is moving.
The ______ is a positive number with units denoting how fast an object is moving.
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The three ways of multiplying vectors are multiplication by a ______, dot product, and cross product.
The three ways of multiplying vectors are multiplication by a ______, dot product, and cross product.
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The dot product of two vectors is mathematically represented as A⃗ . B⃗ = |A||B|______.
The dot product of two vectors is mathematically represented as A⃗ . B⃗ = |A||B|______.
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When the angle θ is 0 degrees, the dot product yields the ______ value.
When the angle θ is 0 degrees, the dot product yields the ______ value.
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The dot product can be either positive, zero, or ______.
The dot product can be either positive, zero, or ______.
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If the angle θ between two vectors is 90 degrees, the dot product equals ______.
If the angle θ between two vectors is 90 degrees, the dot product equals ______.
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The commutative property states that A⃗ · B⃗ = ______ · A⃗.
The commutative property states that A⃗ · B⃗ = ______ · A⃗.
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Unit vectors of the same direction produce a dot product value of ______.
Unit vectors of the same direction produce a dot product value of ______.
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Unit vectors that are perpendicular to each other, such as î and ĵ, yield a dot product of ______.
Unit vectors that are perpendicular to each other, such as î and ĵ, yield a dot product of ______.
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The scalar product of two vectors A and B is a ______ quantity.
The scalar product of two vectors A and B is a ______ quantity.
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The distributive property for dot products can be expressed as (A⃗ + B⃗) · C⃗ = (A⃗ · C⃗) + ______.
The distributive property for dot products can be expressed as (A⃗ + B⃗) · C⃗ = (A⃗ · C⃗) + ______.
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The total linear momentum of a system is the vector sum of the momenta of the individual ______.
The total linear momentum of a system is the vector sum of the momenta of the individual ______.
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The momentum of the system is represented as 𝑝𝑠𝑦𝑠𝑡𝑒𝑚 = ∑ 𝑝𝑖 where 'i' indicates the ______ of the particles being summed.
The momentum of the system is represented as 𝑝𝑠𝑦𝑠𝑡𝑒𝑚 = ∑ 𝑝𝑖 where 'i' indicates the ______ of the particles being summed.
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The centre of mass accelerates as if all the system’s mass were concentrated at that ______.
The centre of mass accelerates as if all the system’s mass were concentrated at that ______.
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The acceleration of the centre of mass is given by the equation 𝑎⃗ = ∑ 𝐹⃗ / ______.
The acceleration of the centre of mass is given by the equation 𝑎⃗ = ∑ 𝐹⃗ / ______.
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The position vector of the centre of mass C of the system is calculated using the formula ______ / (𝑚1 + 𝑚2 + 𝑚3 + ⋯ + 𝑚𝑛).
The position vector of the centre of mass C of the system is calculated using the formula ______ / (𝑚1 + 𝑚2 + 𝑚3 + ⋯ + 𝑚𝑛).
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The ______ of the system is the sum of the masses of all particles involved.
The ______ of the system is the sum of the masses of all particles involved.
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The coordinates of point masses can be represented as (𝑥1 , 𝑦1 , 𝑧1 ), (𝑥2 , 𝑦2 , 𝑧2 ), and so on, marking the ______ of each mass.
The coordinates of point masses can be represented as (𝑥1 , 𝑦1 , 𝑧1 ), (𝑥2 , 𝑦2 , 𝑧2 ), and so on, marking the ______ of each mass.
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For N point masses, the position vector is expressed as ⃗⃗⃗⃗𝑟1 , ⃗⃗⃗⃗𝑟2 , ..., ⃗⃗⃗⃗𝑟𝑛, indicating the positions of each ______ from the origin.
For N point masses, the position vector is expressed as ⃗⃗⃗⃗𝑟1 , ⃗⃗⃗⃗𝑟2 , ..., ⃗⃗⃗⃗𝑟𝑛, indicating the positions of each ______ from the origin.
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If a particle starts from a point 𝑥0, and moves for the time, t, the position equation is 𝑥(𝑡) = 𝑥0 + 𝑣𝑥,0 ______ + 2𝑎𝑥𝑡².
If a particle starts from a point 𝑥0, and moves for the time, t, the position equation is 𝑥(𝑡) = 𝑥0 + 𝑣𝑥,0 ______ + 2𝑎𝑥𝑡².
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The equation for final velocity in terms of initial velocity, acceleration, and time is 𝑣𝑥(𝑡) = 𝑣𝑥,0 + 𝑎𝑥 ______.
The equation for final velocity in terms of initial velocity, acceleration, and time is 𝑣𝑥(𝑡) = 𝑣𝑥,0 + 𝑎𝑥 ______.
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For constant acceleration, the relationship between final and initial velocity can be expressed as 𝑣𝑥²(𝑡) = 𝑣𝑥,0² + 2𝑎∆______.
For constant acceleration, the relationship between final and initial velocity can be expressed as 𝑣𝑥²(𝑡) = 𝑣𝑥,0² + 2𝑎∆______.
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When initial displacement is zero, position simplifies to 𝑥(𝑡) = 𝑣𝑥,0 ______ + 𝑎𝑥𝑡².
When initial displacement is zero, position simplifies to 𝑥(𝑡) = 𝑣𝑥,0 ______ + 𝑎𝑥𝑡².
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The summary for constant acceleration includes the equation 𝑥(𝑡) = 𝑥0 + 𝑣𝑥,0 ______ + 2𝑎𝑥𝑡².
The summary for constant acceleration includes the equation 𝑥(𝑡) = 𝑥0 + 𝑣𝑥,0 ______ + 2𝑎𝑥𝑡².
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When a particle moves with variable velocity, it covers equal displacements in ______ intervals of time.
When a particle moves with variable velocity, it covers equal displacements in ______ intervals of time.
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In the context of motion with variable acceleration, velocity changes in either ______, direction, or both.
In the context of motion with variable acceleration, velocity changes in either ______, direction, or both.
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The area under the graph of the acceleration vs. ______ provides insight about the corresponding velocity.
The area under the graph of the acceleration vs. ______ provides insight about the corresponding velocity.
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Study Notes
Vectors
- Vectors are quantities with both magnitude and direction.
- Vectors combine according to specific rules.
- Examples of physical quantities represented by vectors include force, velocity, acceleration, electric field, and magnetic field.
- A vector is represented by a directed line segment with an arrowhead.
Scalar Definition
- Scalar quantities are those that can be specified by a number and a unit.
- Scalars have magnitude but no direction.
- Examples of scalar quantities include mass, length, time, density, energy, and temperature.
Addition of Vectors
- Vectors can be added using geometrical methods and analytical methods.
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Geometrical Method:
- To represent a vector on a diagram, use an arrow.
- The length of the arrow is proportional to the vector's magnitude.
- The direction of the arrow indicates the vector's direction.
- The arrowhead represents the sense of direction.
- Analytical Method: Using components of vectors.
Rules for Adding Vectors Geometrically
- The resultant vector r is obtained by drawing a line from the tail of the first vector to the head of the second vector.
- a + b = b + a (commutative law)
- (a + b) + c = a + (b + c) (associative law)
Vectors Subtraction/Difference
- For a vector a, the negative -a is a vector with the same magnitude but in the opposite direction.
- a - b = a + (-b)
Equal (Identical) Vectors
- Two vectors are identical if they have the same magnitude and point in the same direction.
- Example: AB = CD
Displacement, Independent of the Path of Motion
- The path of a particle from X to Y need not necessarily be a straight line.
Unit Vectors
- A vector with a magnitude of 1 is a unit vector.
- |â| = 1
- Unit vectors are typically used to specify directions.
Resolution of Vectors
- The geometrical method has limitations in three dimensions.
- For this, the analytical method is useful for resolving vectors into components (components with respect to a coordinate system).
- Components of a vector R along the x- and y -axes can be calculated, using sine and cosine ratios
- ax = |a|cosθ
- ay = |a|sinθ
Component of a Vector
- For a vector A, use components to express a position vector.
- A = axi + ay j + az k
Vector Multiplication
- There are three ways to multiply vectors:
- Multiplying a vector by a scalar. Example kẢ.
- Dot product. Example: Ả⋅ B = |A||B|cosθ.
- Cross product. Example: Ĉ = Ả × B = |A||B| sin θñ
Properties of the Dot Product
- a • b = b • a
- c(a • b) = (ca) • b
- (a + b) • c = a • c + b • c
Summary of Unit Vectors and Dot Product
- î • î = ĵ • ĵ = k • k = 1
- î • ĵ = î • k = ĵ • k = 0
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Description
This quiz covers the fundamental concepts of vectors and scalars, including their definitions, properties, and methods of addition. Test your knowledge on how these quantities work and their applications in physics. Dive into examples of physical quantities and understand their differences.
